In NMR a hydrogen proton magnetic moment is a vector due to spin, but spin 1/2 like protons are spinors, not vectors, so how does spin 1/2 spinor give rise to an actual magnetic moment?
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In quantum mechanics, the magnetic moment $\hat{\vec{\mu}}_s$ is an operator, related to the spin operator $\hat{\vec{S}}$ via $\hat{\vec{\mu}}_s=\gamma \hat{\vec{S}}$. What you observe in experiment is the outcome of evaluating this operator under a spinor wave function $\vert \psi\rangle$ via
$$\vec{\mu}=\langle \hat{\vec{\mu}}_s \rangle = \langle \psi\vert\hat{\vec{\mu}}_s\vert \psi \rangle,$$
where the scalar product is now taken component-wise, such that the resulting expectation value of the magnetic moment $\vec{\mu}$ is a vector in $\mathbb{R}^3$. Note that for spin-1/2 particles the spin operator $\hat{\vec{S}}$ is a vector of Pauli operators $\hat{\sigma}^\alpha$, i.e. $\hat{\vec{S}}=\frac{\hbar}{2}\sum_{\alpha=1}^3 \hat{\sigma}^\alpha \vec{e}_\alpha$ with the canonical Cartesian unit vectors $\vec{e}_\alpha$.
Rudolf Smorka
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